Non-commutative Gelfand-Naimark theorem
Migda, Janusz
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 253-255 / Harvested from Czech Digital Mathematics Library
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We show that if Y is the Hausdorffization of the primitive spectrum of a $C^{\ast }$-algebra $A$ then $A$ is $\ast $-isomorphic to the $C^{\ast }$-algebra of sections vanishing at infinity of the canonical $C^{\ast }$-bundle over $Y$.

Publié le : 1993-01-01
Classification:  46L05,  46L85 
@article{118578,
     author = {Janusz Migda},
     title = {Non-commutative Gelfand-Naimark theorem},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {253-255},
     zbl = {0809.46057},
     mrnumber = {1241734},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118578}
}

Migda, Janusz. Non-commutative Gelfand-Naimark theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 253-255. http://gdmltest.u-ga.fr/item/118578/

Dauns J.; Hofmann K.H. Representation of rings by sections, Mem. Amer. Math. Soc. 83 (1968). (1968) | MR 0247487 | Zbl 0174.05703

Dixmier J. Les $C^{\ast }$-algèbres et leurs representations, Gauthier-Villars, Paris, 1969. | MR 0246136 | Zbl 0288.46055

Dupre M.J.; Gillette M.R. Banach bundles, Banach modules and automorphisms of $C^{\ast }$- algebras, Research Notes in Math. 92, Pitman Advanced Publishing Program, Boston- London-Melbourne, 1983. | MR 0721812 | Zbl 0536.46048

Fell J.M.G. The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. (1961) | MR 0164248 | Zbl 0101.09301

Fell J.M.G. An extension of Macley's method to Banach $\ast $-algebraic bundles, Mem. Amer. Math. Soc. 90 (1969). (1969) | MR 0259619

Tomiyama J. Topological representations of $C^{\ast }$-algebras, Tohôku Math. J. 14 (1962), 187-204. (1962) | MR 0143053